creating buttons for user input

Hi,
My aim is to illustrate lissajous figure of CRO.
The concept is to plot a locus of point whose x & y coordinate vary with time.
In the code given below I have put x=sin(constant x t) , y=cos(1.5 x constant x t)

I have 3 questions
(1)If you will run this , you will see (other than a nice double boomerang animation) a red dot at origin in graph which I want to avoid.
(2)I want to create a slider button for user which replaces 1.5 in above . This way , when slider=1 you will see circle , as frequency multiplies you will see more vertically side by side loops . As frequency diminishes to fraction loop will appear horizontally stacked.
(3)it would be more exciting if there is a slider for changing phase difference .Currently it is 90 degree . As it will decreases the ellipse flattens. becomes straight line for 0 degree.